Since high school I've been a 75-80%+ free throw shooter (and that counts for games). As a point guard I knew very early on that was key. I can still hit 8 of 10, sometimes 10 of 10, most of the time.
It is about routine, routine, routine. That includes balance and follow through.
I learned that from the aforementioned Coach John Lotz. If you don't know who he is/was you should.
John Lotz - Wikipedia
He was a Tar Heel great. Coach Smith mentions him a good deal in
A Coach's Life. When Coach split up with his first wife I believe Coach Lotz was his housemate.